In There are no coherence theorems EJT defines a "coherence theorem" as a theorem that proves maximizing expected utility is the only way to play a game that is not dominated. Ie, any strategy that is not a utility maximisation could be made strictly better. I will make the underlying claim more precise, at least according to my intuition, and prove that it is false in general. I will then discuss what variations of the claim we could think off. There are no coherence theorems was mostly a list of many pre-existing results, none of which proved the underlying claim. The term "coherence theorem" itself gave rise to some discussions and might have been unfortunate. But I agree that something like the following claim has been floating around, more or less implicitely, in multiple documents I read and discussions I had: Intuitive claim Under very little general modelisation assumption, it is in the best interest of any agent playing a game to act as a bayesian utility maximizer. If it is not doing so, the agent could become strictly better by becoming a utility maximizer. If this is true then I find it important, at least somewhat. And if it is false I also wish to know it. An issue with this is that as it stands the claim is too vague to be disproven. There was some discussion in EJT's post claiming that the result he sought was a trivial corollary of the complete class theorem. But even then I wasn't sure what the exact claim was. In this post I will: 1. Give a more precise model for the kind of games we are speaking about and use it to state a conjecture, relfecting the intuitive claim in the general case. 2. Disprove this conjecture with a counterexample. 3. Discuss what alternative precise theorems we might seek to prove or find instead. LaTEX document with a more formal model This post will avoid using too much math. For a more formal discussion of the same ideas see the draft LaTEX document. Iterative game model and conjecture The conjecture bellow